/// <summary>
/// Bestimmt den geometrischen Fehler des angegebenen Vertex in Bezug auf die
/// Fehlerquadrik Q.
/// </summary>
/// <param name="v">
/// Der Vertex, dessen geometrischer Fehler bestimmt werden soll.
/// </param>
/// <param name="q">
/// Die zugrundeliegende Fehlerquadrik.
/// </param>
/// <returns>
/// Der geometrische Fehler an der Stelle des angegebenen Vertex.
/// </returns>
double ComputeVertexError(Double3 v, Double4x4 q)
{
var h = new Double4(v, 1);
//// Geometrischer Fehler Δ(v) = vᵀQv.
return(Double4.Dot(q * h, h));
}
private void OnValueChanged()
{
if (IsSetBlocked)
{
return;
}
var isSliding = XElement.IsSliding || YElement.IsSliding || ZElement.IsSliding || WElement.IsSliding;
var token = isSliding ? this : null;
var value = new Double4(XElement.ValueBox.Value, YElement.ValueBox.Value, ZElement.ValueBox.Value, WElement.ValueBox.Value);
object v = Values[0];
if (v is Vector4)
{
v = (Vector4)value;
}
else if (v is Float4)
{
v = (Float4)value;
}
else if (v is Double4)
{
v = (Double4)value;
}
SetValue(v, token);
}
/// <summary>
/// Writes the Vector4 to the binary stream.
/// </summary>
/// <param name="stream">The stream.</param>
/// <param name="value">The value to write.</param>
public static void Write(this BinaryWriter stream, Double4 value)
{
stream.Write(value.X);
stream.Write(value.Y);
stream.Write(value.Z);
stream.Write(value.W);
}
public void Dot()
{
Double4 a = new Double4(1, 2, 3, 4);
Double4 b = new Double4(1, 2, 3, 4);
Double expected = (Double)(1 + 4 + 9 + 16);
Assert.AreEqual(expected, MathHelper.Dot(a, b));
}
public CurveVertex(Double2 pos, Double4 curve)
{
Position = pos;
CurveCoords = curve;
// Sanity check
//Debug.Assert(!double.IsNaN(curve.X) && !double.IsNaN(curve.Y) && !double.IsNaN(curve.Z), "Problematic curve vertex generated!");
}
public void Bezier(ref Double4 p0, ref Double4 p1, ref Double4 p2, ref Double4 p3, float alpha, out Double4 result)
{
Double4.Lerp(ref p0, ref p1, alpha, out var p01);
Double4.Lerp(ref p1, ref p2, alpha, out var p12);
Double4.Lerp(ref p2, ref p3, alpha, out var p23);
Double4.Lerp(ref p01, ref p12, alpha, out var p012);
Double4.Lerp(ref p12, ref p23, alpha, out var p123);
Double4.Lerp(ref p012, ref p123, alpha, out result);
}
public DoubleCurveVertex(Double2 pos, Double4 curve1, Double4 curve2, bool disjointUnion)
{
Position = pos;
CurveCoords1 = curve1;
CurveCoords2 = curve2;
if (disjointUnion)
{
CurveCoords1.W += 4;
}
Debug.Assert(!double.IsNaN(curve1.X) && !double.IsNaN(curve1.Y) && !double.IsNaN(curve1.Z) && !double.IsNaN(curve1.W));
Debug.Assert(!double.IsNaN(curve2.X) && !double.IsNaN(curve2.Y) && !double.IsNaN(curve2.Z) && !double.IsNaN(curve2.W));
}
private CurveVertex[] CubicBezier_CurveVertices()
{
// Apply the Loop-Blinn method to get the texture coordinates
// Available on https://www.microsoft.com/en-us/research/wp-content/uploads/2005/01/p1000-loop.pdf
// Use the computations in Chapter 4 of the Loop-Blinn paper
// The canonical form of the curve
var c3 = -A + 3 * B - 3 * C + D;
var c2 = 3 * A - 6 * B + 3 * C;
var c1 = -3 * A + 3 * B;
var c0 = A;
// Again the inflection point polynomials, this time the homogeneous form
var d3 = c1.Cross(c2);
var d2 = c3.Cross(c1);
var d1 = c2.Cross(c3);
// The texture coordinates in canonical form
Double4 f0, f1, f2, f3;
void NegateSigns()
{
f0 = f0.NegateX.NegateY;
f1 = f1.NegateX.NegateY;
f2 = f2.NegateX.NegateY;
f3 = f3.NegateX.NegateY;
}
// Check for the "true" cubics first
if (d1 != 0)
{
// Discriminant
var D = 3 * d2 * d2 - 4 * d3 * d1;
// Serpentine or cusp
if (D > -double.Epsilon)
{
// Find the roots of the equation
var dv = d2 >= 0 ? Math.Sqrt(D / 3) : -Math.Sqrt(D / 3);
var q = 0.5 * (d2 + dv);
var x1 = q / d1;
var x2 = (d3 / 3) / q;
var l = Math.Min(x1, x2);
var m = Math.Max(x1, x2);
f0 = new Double4(l * m, l * l * l, m * m * m, 0);
f1 = new Double4(-l - m, -3 * l * l, -3 * m * m, 0);
f2 = new Double4(1, 3 * l, 3 * m, 0);
f3 = new Double4(0, -1, -1, 0);
// Guarantee that the signs are correct
if (d1 < 0)
{
NegateSigns();
}
}
// Loop
else
{
// Find the roots of the equation
var dv = d2 >= 0 ? Math.Sqrt(-D) : -Math.Sqrt(-D);
var q = 0.5 * (d2 + dv);
var x1 = q / d1;
var x2 = (d2 * d2 / d1 - d3) / q;
var d = Math.Min(x1, x2);
var e = Math.Max(x1, x2);
f0 = new Double4(d * e, d * d * e, d * e * e, 0);
f1 = new Double4(-d - e, -d * d - 2 * e * d, -e * e - 2 * d * e, 0);
f2 = new Double4(1, e + 2 * d, d + 2 * e, 0);
f3 = new Double4(0, -1, -1, 0);
// Guarantee that the signs are correct
var h1 = d3 * d1 - d2 * d2;
var h2 = d3 * d1 - d2 * d2 + d1 * d2 - d1 * d1;
var h = Math.Abs(h1) > Math.Abs(h2) ? h1 : h2;
var h12 = d3 * d1 - d2 * d2 + d1 * d2 / 2 - d1 * d1 / 4;
if (Math.Abs(h12) > Math.Abs(h))
{
h = h12;
}
if (d1 * h > 0)
{
NegateSigns();
}
}
}
// Other kind of cusp
else if (d2 != 0)
{
// A single root
var l = d3 / (3 * d2);
f0 = new Double4(l, l * l * l, 1, 0);
f1 = new Double4(-1, -3 * l * l, 0, 0);
f2 = new Double4(0, -3 * l, 0, 0);
f3 = new Double4(0, -1, 0, 0);
}
// Degenerate forms for the cubic - first, a quadratic
else if (d3 != 0)
{
f0 = new Double4(0, 0, 1, 0);
f1 = new Double4(1, 0, 1, 0);
f2 = new Double4(0, 1, 0, 0);
f3 = new Double4(0, 0, 0, 0);
}
// A line or a point - no triangles
else
{
return(new CurveVertex[0]);
}
// Put the texture coordinates back into "normal" form
return(new[]
{
new CurveVertex(A, f0),
new CurveVertex(B, f0 + f1 / 3),
new CurveVertex(C, f0 + (2 * f1 + f2) / 3),
new CurveVertex(D, f0 + f1 + f2 + f3)
});
}
public CurveVertex(Double2 pos, Double4 curve)
{
Position = pos;
CurveCoords = curve;
}
private void SaveState()
{
List<SerializableNode> serializableNodes = new List<SerializableNode> ();
foreach (Node node in Nodes)
{
SerializableNode newNode = new SerializableNode();
newNode.Name = node.Name;
newNode.Position = new Double2 (node.Position.x, node.Position.y);
newNode.HasOutput = node.HasOutput;
newNode.Content = node._content;
newNode.Inputs = new List<int>();
newNode.InputNames = new List<string>();
if (node.Inputs != null)
{
int i=0;
foreach (Node input in node.Inputs)
{
newNode.InputNames.Add (node.InputNames[i]);
if (input != null)
{
newNode.Inputs.Add(Nodes.IndexOf(input));
}
else
{
newNode.Inputs.Add(-1);
}
i++;
}
}
newNode.FloatUserInputs = new List<double>();
newNode.Vector2UserInputs = new List<Double2>();
newNode.ColorUserInputs = new List<Double4>();
foreach (object userInput in node.UserInputs)
{
if (userInput.GetType() == typeof(float))
{
double value = (float)userInput;
newNode.FloatUserInputs.Add(value);
}
if (userInput.GetType() == typeof(Vector2))
{
Double2 value = new Double2(((Vector2)userInput).x, ((Vector2)userInput).y);
newNode.Vector2UserInputs.Add(value);
}
if (userInput.GetType() == typeof(Color))
{
Double4 value = new Double4(((Color)userInput).r, ((Color)userInput).g, ((Color)userInput).b, ((Color)userInput).a);
newNode.ColorUserInputs.Add(value);
}
}
serializableNodes.Add(newNode);
}
string json = JsonMapper.ToJson (serializableNodes);
string actualSavePath = string.Format(WINDOW_SAVESTATE_PATH, SelectedmaterialName) + ".txt";
File.WriteAllText (actualSavePath, json);
}
void IKeyframeAccess <Double4> .SetCurveValue(float curve, ref Double4 value, int component)
{
value[component] = curve;
}
float IKeyframeAccess <Double4> .GetCurveValue(ref Double4 value, int component)
{
return((float)value[component]);
}
void IKeyframeAccess <Double4> .GetDefaultValue(out Double4 value)
{
value = Double4.Zero;
}
public DoubleCurveVertex(Double2 pos, Double4 curve1, Double4 curve2)
{
Position = pos;
CurveCoords1 = curve1;
CurveCoords2 = curve2;
}
public void Linear(ref Double4 a, ref Double4 b, float alpha, out Double4 result)
{
Double4.Lerp(ref a, ref b, alpha, out result);
}
public void GetTangent(ref Double4 value, ref Double4 tangent, float lengthThird, out Double4 result)
{
result = value + tangent * lengthThird;
}